Quadratic Equations: common misconceptions

If your child says… “Any equation showing a squared term is quadratic.”

Ask together

If the squared terms cancel completely, what squared term remains?

What’s true

A squared term must survive after simplifying, with no higher powers remaining.

If your child says… “A number is a root if it divides the constant.”

Ask together

If substitution leaves unequal sides, can that number be a root?

What’s true

Substitution must make the two sides equal.

If your child says… “The roots are minus one and minus two.”

Ask together

Does putting minus one into the first bracket make it zero?

What’s true

Solve each bracket equal to zero instead of copying its number.

If your child says… “Both roots must be possible widths.”

Ask together

Could this rectangle have a width of minus three centimetres?

What’s true

An equation's roots still need checking against what the unknown measures.

If your child says… “I can ignore the minus when taking the square root.”

Ask together

Which real number could give minus four when squared?

What’s true

Squaring a real number never produces a negative result.

If your child says… “Real roots always need a zero discriminant.”

Ask together

When the discriminant is positive, can the formula still give real answers?

What’s true

Real roots occur with either a zero or a positive discriminant.